Multifractal systems are common in nature, especially geophysics. They include fully developed turbulence, stock market time series, real world scenes, the Sun’s magnetic field time series, heartbeat dynamics, human gait, and natural luminosity time series. Models have been proposed in various contexts ranging from turbulence in fluid dynamics to internet traffic, finance, image modeling, texture synthesis, meteorology, geophysics and more. The origin of multifractality in sequential (time series) data has been attributed, to mathematical convergence effects related to the central limit theoremthat have as foci of convergence the family of statistical distributions known as the Tweedie exponential dispersion models[2] as well as the geometric Tweedie models.[3] The first convergence effect yields monofractal sequences and the second convergence effect is responsible for variation in the fractal dimension of the monofractal sequences.[4]

From a practical perspective, multifractal analysis uses the mathematical basis of multifractal theory to investigate datasets, often in conjunction with other methods of fractal analysis and lacunarity analysis. The technique entails distorting datasets extracted from patterns to generate multifractal spectra that illustrate how scaling varies over the dataset. The techniques of multifractal analysis have been applied in a variety of practical situations such as predicting earthquakes and interpreting medical images."

According to the IPCC, only man-made CO2 can possibly explain the global temperature record since 1950. However, IPCC models are unable to model natural variability including ocean oscillations, solar amplification mechanisms, and internal variability, and thus these factors cannot be excluded as possible causes. The fractal model as described in this study might be a potential way to model natural internal variability of the climate system, and suggests that internal variability alone could account for climate change since 1850, without any contribution from man-made CO2. Could multifractals be another cause for the "pause?"

The global monthly temperature anomaly time series for the period 1850–2012 has been investigated in terms of multifractal detrended fluctuation analysis (MF-DFA). Various multifractal observables, such as the generalized Hurst exponent, the multifractal exponent, and the singularity spectrum, are extracted and are fitted to a generalized binomial multifractal model consists of only two free parameters. The results of this analysis give a clear indication of the presence of long-term memory in the global temperature anomaly time series which causes multifractal pattern in the data. We investigate the possible other source(s) of multifractality in the series by random shuffling as well as by surrogating the original series and find that the probability density function also contributes to the observed multifractal pattern along with the long-memory effect. Surprisingly, the temperature anomaly time series are well described by the two-parameter multifractal binomial model.

3 comments:

In effect, multifractals state that the system is chaotic, nothing can be predicted with certainty.

Just like my professor said Put a meteorologist in a closet with tables of weather for the last hundred years and a PC and he will do just as well as a fully staffed weather bureau with the most modern technology.

Not really. My reading of the paper is that this is a model of the spikes in the detrended data -- not a way of analyzing the trend. In other words, this has nothing to do with "global warming," but instead has to do with characterizing what we see as noise.

This paper wound not explain either the long term warming trend or the "pause." It would explain how the anomalies vary around the long term trend and/or the "pause." The paper has nothing to do with global warming, because it is detrended out -- at least as I read it.